Details

sample86.0ms

Algorithm

intervals

Results

20.0ms	59×	body	640	valid
19.0ms	259×	body	80	nan
15.0ms	36×	body	1280	valid
12.0ms	137×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	15
2	15
1	11
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize55.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.6b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
897×	`*-un-lft-identity`
782×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
576×	`sqrt-prod`
73×	`distribute-lft-out`
56×	`div-inv`
46×	`sqrt-div` `associate-/r/`
25×	`difference-of-squares`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube`
6×	`pow-flip` `associate-/l*`
5×	`add-log-exp`
4×	`div-exp`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 772

Calls

3 calls:

17.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
57.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series195.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ 1 (sqrt (+ x 1)))
46.0ms	(/ 1 (sqrt x))
103.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.8s

Counts

781 → 781

Iterations

Iter	Nodes
2	2361
1	1399
0	643

prune1.8s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 18.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt x))
0.5b	(* (cbrt (sqrt x)) (cbrt (sqrt x)))
28.9b	(fma (/ (sqrt 1) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (sqrt 1) (cbrt (sqrt x))) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
30.8b	(fma (- (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

46×	`cbrt-prod`
40×	`add-sqr-sqrt`
23×	`sqrt-prod`
18×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
7×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `fma-udef`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

2.0ms	(cbrt (sqrt x))
19.0ms	(* (cbrt (sqrt x)) (cbrt (sqrt x)))
0.0ms	(fma (/ (sqrt 1) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (sqrt 1) (cbrt (sqrt x))) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
1.0ms	(fma (- (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

series952.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt (sqrt x))
201.0ms	(* (cbrt (sqrt x)) (cbrt (sqrt x)))
245.0ms	(fma (/ (sqrt 1) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (sqrt 1) (cbrt (sqrt x))) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
313.0ms	(fma (- (/ (sqrt 1) (cbrt (sqrt (+ x 1))))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

simplify4.4s

Counts

110 → 110

Iterations

Iter	Nodes
3	4006
2	1206
1	421
0	176

prune925.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 18.0b

localize38.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
11.0b	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

231×	`*-un-lft-identity`
203×	`add-sqr-sqrt`
189×	`prod-diff`
180×	`times-frac`
172×	`add-cube-cbrt`
106×	`sqrt-prod`
89×	`unpow-prod-down`
33×	`sqr-pow`
25×	`distribute-lft-out`
16×	`sqrt-div` `associate-/r/`
15×	`difference-of-squares`
9×	`div-inv`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `fma-neg`
6×	`add-exp-log`
4×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`pow-flip` `associate-/l*`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

2 → 282

Calls

2 calls:

10.0ms	(/ 1 (sqrt (+ x 1)))
45.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

series120.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ 1 (sqrt (+ x 1)))
89.0ms	(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))

simplify2.5s

Counts

288 → 288

Iterations

Iter	Nodes
3	3435
2	1607
1	901
0	388

prune946.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 18.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
0.5b	(* (pow x -1/2) (pow x -1/2))
1.0b	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
9.8b	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
168×	`times-frac`
166×	`*-un-lft-identity`
87×	`add-cube-cbrt`
86×	`sqrt-prod`
58×	`add-exp-log`
48×	`swap-sqr`
34×	`associate-r` `associate-l` `unswap-sqr`
28×	`distribute-lft-out`
27×	`pow1`
25×	`prod-exp`
24×	`pow-flip`
20×	`add-cbrt-cube`
18×	`unpow-prod-down`
17×	`div-exp`
12×	`div-inv`
10×	`associate-/r/` `pow-prod-up` `sqr-pow`
8×	`rec-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `inv-pow`
7×	`difference-of-squares`
6×	`pow-to-exp` `pow-prod-down` `pow-exp` `pow-sqr` `add-log-exp`
5×	`cbrt-undiv` `associate-/r*` `flip3-+` `cbrt-unprod` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `flip3--` `*-commutative` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `prod-diff` `associate-l/` `associate-r/` `un-div-inv`

Counts

4 → 298

Calls

4 calls:

47.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
14.0ms	(* (pow x -1/2) (pow x -1/2))
68.0ms	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
12.0ms	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
11.0ms	(* (pow x -1/2) (pow x -1/2))
156.0ms	(/ (- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (pow x -1/2) (/ 1 (sqrt (+ x 1)))))
51.0ms	(- (* (pow x -1/2) (pow x -1/2)) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify3.3s

Counts

310 → 310

Iterations

Iter	Nodes
2	3109
1	1183
0	424

prune982.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.7b

regimes28.0ms

Accuracy

99.9% (0.0b remaining)

Error of 5.5b against oracle of 5.5b and baseline of 25.8b

bsearch69.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	318690.85562629136	7911.288097968324

simplify6.0ms

Iterations

Iter	Nodes
2	36
1	36
0	27

end0.0ms

sample3.0s

Algorithm

intervals

Results

727.0ms	1830×	body	640	valid
610.0ms	8060×	body	80	nan
534.0ms	649×	body	320	valid
518.0ms	1147×	body	1280	valid
334.0ms	4063×	body	80	valid
44.0ms	311×	body	160	valid